Question

1. the graph shown is that of ( y = g(x) ). which of the following is the equation for ( g(x) )?

a. ( g(x) = \frac{3}{4}x + 3 )
b. ( g(x) = \frac{3}{4}x - 3 )
c. ( g(x) = -\frac{3}{4}x + 3 )
d. ( g(x) = -\frac{3}{4}x - 3 )

Explanation:

Step1: Identify slope-intercept form

The linear equation form is $y=mx+b$, where $m$ is slope, $b$ is y-intercept.

Step2: Find y-intercept ($b$)

From the graph, the line crosses the y-axis at $(0, -3)$, so $b=-3$.

Step3: Calculate slope ($m$)

Use points $(4,0)$ and $(0,-3)$:
$$m=\frac{0 - (-3)}{4 - 0}=\frac{3}{4}$$

Step4: Build the equation

Substitute $m=\frac{3}{4}$ and $b=-3$ into $y=mx+b$:
$g(x)=\frac{3}{4}x - 3$

Answer:

B. $g(x)=\frac{3}{4}x - 3$